On the stability properties of polynomials with perturbed coefficients

Given a polynomial
P_{c}(S) = S^{n} + t_{1}S^{n-1} + ... t_{n} = 0
which is Hurwitz or
P_{d}(Z) = Z^{n} + t_{1}Z^{n-1} + ... t_{n} = 0
which has zeros only within or on the unit circle, it is of interest to know how much the coefficients t
j
can be perturbed while preserving the stability properties. In this note, a method is presented for obtaining the largest hypersphere centered at
t^{T} = [t_{1} ... t_{n}]
containing only polynomials which are stable.